Explain the purpose of using a counter.
29. What are the two types of counters?
30. Describe the operation principle of an up counter.
31. Draw the schematic symbols for up counters and their contacts.
32. Describe the operation principle of a down counter.
33. Draw the schematic symbols for down counters and their contacts.
34. Compare and contrast circuit design and circuit analysis.
35. List the eight-step procedure of circuit analysis.
Number Systems and Codes
PLCs use numbers to implement control functions. We will introduce four commonly used number systems, digital code standards, and PLC data formats in this chapter. The four number systems are binary, octal, decimal, and hexadecimal systems. Number conversions between two different number systems are presented. The digital code standards include binary coded decimal (BCD), Gray code, and ASCII code. The format in which data is represented determines how the binary pattern is to be interpreted. The basic word format, decimal numbers, negative numbers, and floating point decimal numbers to represent numeric values in PLCs are presented.
3.1 Number Systems
PLCs are digital machines that rely on numbers to implement their basic operations and store various types of information. A number system is a standardized scheme whereby a fixed set of symbols is used to represent numeric values. Each number system has the following characteristics:
•Has a base number
•Has a set of symbols
•Is used for counting
The base number or radix of a number system determines the maximum number of unique symbols used by that number system. The base 10 number system, for instance, has the number 10 as its base and has ten unique symbols, 0 through 9. The largest valued symbol has a value of one less than the base.
PLCs use four number systems: base 2, base 8, base 10, and base 16. These four number systems are also referred to as binary (base 2), octal (base 8), decimal (base 10), and hexadecimal (base 16). Table 3.1 summarizes the base and counting symbols of these four commonly used number systems.
Extra digits are used to express any number that is greater than the base number. The place value, also referred to as position weight, is used to assign a value to each position of a number. The second digit from the right in a base 10 number, for instance, is assigned a place value of 10. The third digit from the right in a base 10 number has a place value of 100.
Table 3.1: Four number systems
| Number System | Base | Counting Symbols |
|---|---|---|
| Binary | 2 | 0, 1 |
| Octal | 8 | 0, 1, 2, 3, 4, 5, 6, 7 |
| Decimal | 10 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 |
| Hexadecimal | 16 | 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F |
3.2 Decimal Number System
The decimal number system uses the base number 10. It has a total of 10 unique symbols (0, 1, 2, 3, 4, 5, 6, 7, 8, and 9) to count the numbers. Multiple-digit numbers are used to count any number greater than 9. The position of each digit in a number determines its weighted value. The zero position is the right-most position and increments by one to the left. The right-most position is the least significant position, and the left-most is the most significant position. The weighted-value of each position can be expressed as the base raised to the power of position. In decimal number system, the position weights from right to left are 1 (or 100), 10 (or 101), 100 (or 102), 1000 (or 103), etc. Table 3.2 illustrates the position,
